Workaround to keyframe the world setting?
You could merge all your world settings into one world setting and animate node properties.

You could use a mix node, as shown below, to animate between different HDR images and animate the factor from 0 to 1 to switch between them. Adding additional mix nodes after the first one would allow you mix between as many HDR images as you want. 



Keyframes can be inserted on node properties in the same way as other properties, by pressing I while the cursor is over that value.

As you said that some other nodes were also different in each setup, you could either animate the values for each node or again use a mix node to switch between whole networks of nodes instead of just an environment node as shown below.



Note that to mix 2 background shaders a 'Mix Shader' node is used instead of 'MixRGB'.

Nodes can be copied from one world setting to another with Ctrl+C and Ctrl+V